Queueing systems

The program comes with its own job queue system. Jobs are submitted to this queue via a script, which can be edited to utilize third-party batch-queuing systems instead. 

The calculation setup screens list a good selection of the options that are most widely used. However, it is not a complete list. The user also chooses which queue to use on the remote machine and can set queue resource limits. All of this is turned into a script with queue commands and the job input file. The user can edit this script manually before it is run. Once the job is submitted, the inputs are transferred to the server machine, the job is run and the results can be sent back to the local machine. The server can be configured to work with an NQS queue system. The system administrator and users have a reasonable amount of control in configuring how the jobs are run and where files are stored. The administrator should look carefully at this configuration and must consider where results will be sent in the case of a failed job or network outage. 

Gaussian is designed to execute as a batch job. It can readily be used with common batch-queueing systems. The program may be purchased as source code or executables and comes with hundreds of sample input and output files. These may be employed as examples of how to construct inputs. They may also be employed to verify that a compilation from source code was successful. In our experience, such verification is essential. 

Alternatively, the user can construct ASCII input files manually. The file format includes many numerical flags to control the type of calculation. The researcher should plan on investing some time in learning to use the program in this way. Jaguar can be executed from the command line, making it possible to use batch processing or job queue systems. 

Gaussian users will find that Q-Chem feels familiar. The ASCII input format is a bit more wordy than Gaussian it is more similar to GAMESS input. The output is very similar to Gaussian output, but a bit cleaner. The code can easily be used with a job-queueing system. 

AMPAC can also be run from a shell or queue system using an ASCII input file. The input file format is easy to use. It consists of a molecular structure defined either with Cartesian coordinates or a Z-matrix and keywords for the type of calculation. The program has a very versatile set of options for including molecular geometry and symmetry constraints. 

There is a screen to set up the calculation that has menus for the most widely used functions. Many users will still need to know many of the keywords, which can be typed in. There was no default comment statement, so the input file created would not be valid if the user forgot to include a comment. A calculation can be started from the graphic interface, which will be run interactively by default. The script that launches the calculation was not too dilficult to modify for use with a job-queueing system. 

L. Kleinrock, Queueing Systems, Vol. I, Theory. Wiley, New York, 1976. 

Prior Scientific Instruments Ltd., London Rd., Bishop s Stanford, Herts. CM23 5NB. Queue Systems (see Camlab.). 

In a departure from the Soviet three-queue shopping system (the first queue to decide what to buy, the second to pay and receive a receipt, and the third to exchange the receipt for the goods purchased), in which customers often had to demand service from cashiers, McDonald s introduced a single-queue system in which cashiers waited on customers and advertised when they were available to serve the next customer with the words Svobodnaia kassa. For more discussion of the nature and impact of McDonald s in post-Soviet Russia, see Caldwell 2004a. 

Identical Servers Suppose there are c parallel servers with identical capabilities. The mean time between arrival of jobs is 1/A and the mean time to serve a job is 1/p.. Jobs wait in a single queue and the first job in the queue is allocated to the first free server. Let p = A/cp.. Then with general arrivals and general service time distributions there are no exact results. One approach is to approximate the system by a G/GIl queue and then modify the performance measures by the relationship between M/M/c and Ml Ml I results. When the multiple server system is represented by a G/G/l queue, the arrival process at the queueing system is unchanged but the service time of the... 

The flow line is modeled by a tandem queueing system with m stages and with finite buffer capacities b, ..., b with bj = Zi + where is the number of spaces in buffer i, and exponentially distributed processing times with mean 1/fjLj, i = 1,2,. m. The Jobs arrive at the flow line according to a Poisson process with rate A. 

IX, b) be the mean number of customers in an M/M/l/b queueing system with arrival rate A, service rate fx, and buffer capacity b. If p = /p.,... 

Ml MU and M/M/c queueing systems can be directly applied to this queueing network model. Particularly when there is only a single machine at each machine center (i.e. Cj = 1, i = 1,.. . , m), we have... 

Let Tj be a generic random variable representing the stationary distribution of the number of ptuts in an MIM(n)ll queueing system with arrival rate Aj = AU and state-dependent service rate fJLjrjikj) when there are kj parts in the system (k = 1,2,... ). A can be any value that guarantees the existence of a stationary distribution for the M/M n)/1 queue. For example, if r j) = min ti, c, that is, we have Cj parallel servers at service center i, then we require that or equivalently A < fjLfij/... 

Hence we see that the total number of parts in the open queueing network is the same in distribution as that in an M/M(n)/1 queueing system with arrival rates A and state dependent service rates TH(n), n = 1,2,... For the purpose of analyzing the aggregate behavior of the total number of parts in the system, we can aggregate the whole FMS and replace it by an equivalent single-stage server with state dependent service rates equal to the production rates. 

Gordon, W. J., and Newell, G. F. (1967), Qosed Queueing Systems with Exponential Servers, Operations Research, Vol. 15, pp. 254-265. 

Let the outstanding orders correspond to the jobs in the queueing system. In the inventory system, each of these orders will materialize (or arrive —become available to supply demand) after a lead time. This corresponds to a queueing system with an infinite number of servers, so that any job will be served immediately on arrival. Hence, the overall cycle time of each job in the system is simply its service time, which corresponds to the lead time of orders in the inventory system. 

Let N be the number of jobs in the queueing system in steady state. This, as explained above, represents the number of outstanding orders. If N < R, then there are R — N units of on-hand inventory. If N > R, then we know there are N — R units of back orders R units of demand have been supplied with on-hand inventory, while the remaining N - R units are back ordered. Hence, with I and B denoting the on-hand inventory and the back orders, respectively, and with [x]+ denoting max x, 0, we have... 

Suppose demand follows a Poisson process with rate A, and suppose the lead time is L, the time it takes to process and finish an order. Then the queueing system in question is an M/GI > model (see, e.g., Wolff 1989), and it is known that N follows a Poisson distribution with mean p = AE(L). That is,... 

Let D(t) be the demand in period t, t = 1, 2,. . . Suppose demand (per period) over time is independent and identically distributed. Let L denote the lead time to flU each replenishment order. The number of outstanding orders, as explained in Section 2.1, is equal to the number of jobs, N, in an infinite-server queueing system. In particular, if the per-period demand follows a Poisson distribution, then N also follows a Poisson distribution with mean E(N) = E(D) E(L) (= p in Section 2.1 here D denotes the generic per-peiiod demand). Since N follows a Poisson distribution, we know Var(A0 = E(A0-... 

This clearly relates to the base-stock control mechanism. In particular, K = R—any unit of demand will trigger production (or replenishment), whereas when the finished goods inventory reaches K, production will be suspended. Kanban, however, has the additional feature of blocking arrivals (of demand) when the on-hand inventory drops down to zero, that is, when aU K cards are associated with outstanding orders, which is the situation in (2) above. Hence, kanban corresponds to a finite queueing system with K being the buffer capacity—the upper limit on the total number of jobs allowed in the system. 

In this subsection, we develop a very simple queueing model. This model is a Markov chain IXf) representing the number of jobs present in a queueing system observed at regular discrete times t = 0, 1, 2,. . . The state space is 0, 1, 2,. . . . There are two types of transitions possible arrivals and departures. We write p for the probability that a job arrives in the next time step. We write q for the probability that a job will complete service in the next time step, assuming that there is at least one job present (L(t) > 0). If we write r for 1 — p — q, which is the probability of no state change when there is at least one job present, then the transition matrix of the chain is... 

Sennott, L. I. (1999), Stochastic Dynamic Programming and the Control of Queueing Systems, John Wiley Sons, New York. 

Kleinrock, L. 1975. Queueing Systems. Vol. 1. Toronto John Wiley Sons,pp. 71-72, 119-134. 

Batch-and-queue system Refers to a production management system that relies on large batches of material. This leads to large queues while waiting to complete a production step. Such systems are characterized by high work in process inventory and low velocity production. 

S. Stidham. Optimal control of admission to a queueing system. IEEE Trans. Automatic Control, AC-30 705-713, 1985. 

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